The 27-year-old joined the Gunners in a deadline-day switch from relegated Palermo having enjoyed a loan spell the preceding season with Serie A side Fiorentina - keeping 11 clean sheets in the process.
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"He comes to the club at the top of his game. It was a very good deal for us at a good moment, I think it was a no-brainer as well," the 63-year-old told Arsenal Player.
"With two goalkeepers available for the Premier League and all the competitions we face, we felt we were a bit short because sometimes you have injuries and sometimes you need to rest one of the goalkeepers.
"At the moment, Wojciech is number one unless I decide otherwise. They are all competing for the place of the number one. At the moment, one and two are Wojciech and Fabianski. After, maybe I will rotate.
"Viviano is a highly-rated goalkeeper in Italy so we have three goalkeepers that are very compact quality-wise."